A circular tank of diameter 2m is dug and the earth removed is spread uniformly all around the tank to form an embankment 2m in width and 1.6m in height. Find the depth of the circular tank 
 

Asked by Pratyush Singh | 7th Jun, 2017, 01:13: PM

Expert Answer:

begin mathsize 16px style Let space the space depth space of space the space circular space tank space be space straight h space straight m.
Diameter space of space the space tank equals 2 space straight m
rightwards double arrow Radius space of space the space tank equals 1 space straight m space equals space straight r
Thus comma space volume space of space the space tank equals πr squared straight h equals straight pi cross times 1 cross times straight h equals πh
Now comma space volume space of space the space embankment
equals Volume space of space hollow space cylinder space having space height space 1.6 space straight m
equals straight pi left parenthesis straight R squared minus straight r squared right parenthesis straight H
equals straight pi left square bracket left parenthesis 1 plus 2 right parenthesis squared minus left parenthesis 1 right parenthesis squared right square bracket cross times 1.6
equals straight pi left parenthesis 9 minus 1 right parenthesis cross times 1.6
equals 12.8 straight pi
Now comma
Volume space of space tank equals Volume space of space embankment
rightwards double arrow πh equals 12.8 straight pi
rightwards double arrow straight h equals 12.8 space straight m end style

Answered by Rashmi Khot | 7th Jun, 2017, 02:34: PM